OFDM based on Discrete Fourier Transform (DFT) processing is a popular modulation approach in developing and planned wireless communication systems, such as 3GPP LTE, IEEE WiMAX 802.16x, IEEE WiFi 802.11x, etc. DFT-based modulation provides efficient and practical channel equalization algorithms, when used for the transmission of multi-carrier signals, like the OFDM signals used in LTE and LTE-Advanced. Furthermore, multiple access solutions that allow flexible resource allocation (e.g., Orthogonal Frequency Division Multiple Access or OFDMA) can be implemented in conjunction with the use of DFT-based and other OFDM signals structures.
However, the OFDM signal is characterized by large fluctuations of its power envelope that result in occasional spikes in the power of the signal—for example, such signals are characterized by having a relatively high Peak-to-Average-Power-Ratio (PAPR) or high “Cubic Metric” (CM). The large power fluctuations in high PAPR/CM signals impose significant design requirements on the radiofrequency (RF) power amplifier (amplifier chains) used to transmit OFDM signals. In particular, the large power fluctuations require the RF Pas to be operated with significant back-off, to have sufficient margin for accommodating the power peaks in the OFDM signal. More generally, the overall transmit signal chain must be “dimensioned” in one or more senses, to handle the worst-case power peaks of the OFDM signal.
For energy, cost, or space critical designs (e.g., mobile devices) the power back-off margins required by DFT-OFDM lead to an inefficient solution. Therefore, modifications to the standard OFDM system have been introduced, to obtain systems with roughly the same advantages of DFT-OFDM over single carrier systems, but with more compressed signal dynamics. The two most popular techniques are Distributed Single Carrier OFDMA (sometimes also called B-IFDMA) and Localized Single Carrier (LOC-SC) OFDMA, also referred to as DFTS-OFDM. LOC-SC-OFDMA has been adopted for 3GPP LTE, to improve the efficiency of uplink transmissions.
In both LOC/DIST-SC-OFDMA, the Inverse DFT (IDFT) modulator at the transmitter is preceded by a standard DFT precoder. The two techniques differ in the way the outputs from the DFT precoder are mapped to the inputs on the IDFT. Inverse processing is correspondingly performed at the receiver side, and linear equalization techniques can be performed in the same way as for conventional OFDM/OFDMA. As a further alternative, researchers have investigated new modulation systems based on the use of Discrete Cosine Transform (DCT) processing. See, e.g., P. Tang, N. C. Beaulieu, “A Comparison of DCT-Based OFDM and DFT-Based OFDM in Frequency Offset and Fading Channels,” IEEE 2006.
Further work has touched on the use of DCT-based transmission “precoding” in the OFDM context, in the interest of improving system performance through, e.g., lower Bit Error Rates (BERs). See, e.g., de Fein, C. and Fagan, A. D., “Precoded OFDM—An Idea Whose Time Has Come,” ISSC 2004, Belfast. Additional work on precoding in the context of DCT-based OFDM appears in, e.g., Wang, Zhengdao and Giannakis, Georgios, “Linearly Precoded or Coded OFDM against Wireless Channel Fades?” Third IEEE Signals Processing Workshop, Taiwan, 2001.
Broadly, with DCT-based OFDM, the transmitter employs a DCT (or, equivalently, an IDCT) for modulation processing. Compared to conventional DFT-based OFDM systems equalization in the DCT-OFDM context is more complex. However, DCT-based OFDM systems retain the attractive channel diagonalization properties of DFT-OFDM, based on employing a symmetric Cyclic Prefix (CP) and a pre-filter at the receiver. See, e.g., N. Al-Dhahir, H. Minn, S. Satish, “Optimum DCT-Based Multicarrier Transceivers for Frequency-Selective Channels,” IEEE 2006.
While DCT-based OFDM offers a number of promising characteristics, the underlying signals used in an a DCT-OFDM system still experience potentially large envelope fluctuations that are difficult to handle within the practical limits of hardware. Furthermore, there appears to be significant work remaining in developing efficient multiple access techniques that allow the co-scheduling of multiple users, while still offering an advantageously low PAPR/CM.